Question: Which of the following numbers is a factor of 51? ${3,7,9,12,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $51$ by each of our answer choices. $51 \div 3 = 17$ $51 \div 7 = 7\text{ R }2$ $51 \div 9 = 5\text{ R }6$ $51 \div 12 = 4\text{ R }3$ $51 \div 14 = 3\text{ R }9$ The only answer choice that divides into $51$ with no remainder is $3$ $ 17$ $3$ $51$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $3$ are contained within the prime factors of $51$ $51 = 3\times17 3 = 3$ Therefore the only factor of $51$ out of our choices is $3$. We can say that $51$ is divisible by $3$.